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Finding the Third Proportional to 7,823 and 19,422

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Solution

The third proportional to 7,823 and 19,422 is: 48,218.60

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,823 : 19,422 = 19,422 : x
  2. Step 2: Convert to fraction form
    7,823/19,422 = 19,422/x
  3. Step 3: Cross multiply
    7,823x = 19,422 × 19,422
  4. Step 4: Simplify right side
    7,823x = 377,214,084
  5. Step 5: Solve for x
    x = 377,214,084/7,823
  6. Step 6: Final answer
    x = 48,218.60

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Why These Related Problems?

These problems maintain the same ratio (2.48) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.